The present invention relates to a method for finding an optimal set-point for machines and processes. More particularly, the invention relates to a method for recalibrating the constants of an existing model of a machine and process and for finding optimal set-points for operating with the same. Furthermore, the invention relates to a controller, which utilizes the said method for establishing the optimal set point for a machine.
In any manufacturing process, there are process machines which take multiple inputs (such as gases, materials, power, etc.), arrange local environments (such as pressure, temperature, etc.), and change either the shape or some set of properties of the operant material(s). The desired output is a specific arrangement of new properties (e.g., index of refraction, stress, geometry, etc.) on the operant material, and are called herein either the output, the product, or the goal. It is axiomatic that the output goals must be given in terms of acceptable ranges of variations from the desired goal.
In order to predict the output of a machine (hereinafter, whenever the term xe2x80x9cmachinexe2x80x9d is used, it should be understood that it may also refer to a process) for a specific set of inputs, there is a need to provide a model of the machine. The model may consist of a set of smaller models which predict one or more properties of the output.
One common type of a model is the physical model. A physical model comprises a set of mathematical functions and formulas arising from first principle physics that describe the behavior and the operation of the machine. These models often contain some calibration constants which are related to some physical characteristic of the process but for which the first principle knowledge is either limited or lacking. These constants are adjusted to allow the model to properly simulate the process.
Other types of models are data based models (sometimes also referred to in the art as xe2x80x9cstatistical modelsxe2x80x9d) which only try to fit experimental data from the machine. These models are constructed by means of carrying out many experiments and accumulating a large amount of raw data relating to the characteristics of the output product versus different sets of inputs. They are generally used in cases where the physical model is either not known or becomes very complicated and thus it is difficult to evaluate its many constants. These data based models treat the machine as a xe2x80x9cblack boxxe2x80x9d, and try to predict the properties of the output product versus the inputs, based on experimental results. Thus the constants also allow the model to simulate the process but, unlike the physical model, they are not connected to any physical characteristic. For this reason, physical models are usually more accurate.
The variables of the function(s) of the model (hereinafter, the x""s) are the inputs to the machine, which should be determined for any specific output desired. One combination of machine settings for providing a specific output which includes the inputs and environment variables, is called a set-point or set-up. In virtually every industrial application or controller that uses some sort of predictive model, the constants are determined from a data set with the number of set-points equal to or greater than the number of undetermined constants in the model. In some applications, data is abundantly available from continuous input from sensors. In others the data is difficult or expensive to obtain. In such cases, the xe2x80x98Design of Experimentsxe2x80x99 (DOE) method of conducting the experiments describes the conditions to obtain the most data from the fewest experiments. Whether the data is abundantly available or a DOE set of experiments is being performed, recalibration of the model requires a complete new data set. In the continuously available data mode, this presents no difficulty. But in the more frequent DOE case, another expensive data set generation is required. A unique feature of the present invention is that only one new data point is required in order to update the model. While the process of the present invention is applicable to both types of data environments, the operation will be described most fully for the latter, more difficult case.
Since the output product must be given in terms of an acceptable range of variation from the desired goal, it also follows that there are many machine set-points that give outputs in the acceptable range. It is therefore desired to find, for each output, a set-point, of the many available, which is optimal in some sense. For example, one criterion could be to find a set-point in which the product is most robust to variations in the inputs. By this it is meant that some of these set-points will cause the characteristics of the output product to be more sensitive to variations in the inputs than the others, as a small change in the input value may cause the product to be out of the acceptable range. It should thus be desirable to choose the set-point for which small variations cause the least change in the output product. Other criteria could include asking for the new set-point to be as close as possible to the last known set point. In the present procedure, virtually any set of criteria or constraints can be applied to select an optimal set-point.
Obviously, there is no model that can stay forever accurate. Any machine changes over time, some of its parts wear out and have to be replaced, other parts may become dirty, and a maintenance procedure has to be carried out from time to time. Thus the constants of the model have to be recalibrated from time to time in order to compensate for any changes.
To do this recalibration, the prior art required a long series of tests to be conducted in order to reevaluate the constants of a model. In any case, the procedures of the prior art for updating the model and finding a new set-point for operating the machine are non-productive, and expensive.
U.S. Pat. No. 5,740,033 discloses a design of an interactive controlling device for a manufacturing process. This patent provides an algorithm for devising the desired set-point or operating conditions of the machine. In particular, the controlling device includes a physical process model and an independent disturbance physical model. An executive sequencer periodically sends recorded data to the process model, which in turn makes predictions as to desired set-points for the machine. This patent uses large data sets that are continuously provided to the inputs by sensors. Furthermore, the interactive controller of this patent is aimed at making dynamic changes in machine settings to control uniformity of product.
U.S. Pat. No. 4,577,280 discloses a control system for distributing a fluid flow. The object of the system in this patent is to optimally distribute a fluid in a steam-generating plant. The system uses an algorithm for predicting the best fluid distributions, in essence, a set-point. However, if the model is changed, and in order to determine a suitable set-point again, a large data set is required, which is difficult and expensive to obtain.
U.S. Pat. No. 4,835,690 discloses an expert system for medical imaging scanning, setting up, and scheduling. This patent relates to standardizing image quality in medical diagnostic imaging. Several machine settings are to be adjusted in order to achieve this end. However, a large data set has to be used in order to compute the constants, and the resulting model can be updated only by means of another complete set.
U.S. Pat. No. 5,774,761 discloses a machine set-up procedure using multivariate modeling and multiobjective optimization. This patent deals mainly with machine settings in electrostatographic printing for controlling image quality. The procedure shows how a model is calibrated and then is used for computing an optimal set of machine settings. The model suitable for this procedure is completely statistical, and the calibration is performed with a large data set in a DOE manner rather than a single point.
It is therefore an object of the present invention to provide in optimal set-point for the machine operation in a fast and easy manner, requiring the least possible number of experiments to achieve the optimal set-point.
It is another object of the invention to provide a method for recalibrating the model of a machine process, when needed.
More particularly, according to the method of the present invention, in most cases carrying out fewer than four tests is sufficient for updating the model, and for finding a new set-points for operating the machine with the updated model.
The present invention relates to a method for optimizing a machine set-point, which comprises the following steps: (a) Defining allowed ranges for the properties of the output product, the ranges of the possible machine set-points and optimal set-point criteria; (b) Carrying out calibration of the model of the machine for finding updated constants for the machine model; (c) Using the updated constants in the machine model, finding all set-points that will provide a product whose properties are within the allowed ranges; (d) Carrying out an optimization procedure to find from all the set-points found in step c, one optimized set-point; (e) Operating the machine at the optimized set-point found in step d, and obtaining a new output product; (f) Comparing the properties of the new output product to the allowed ranges; (g) If the properties of the output product are within allowed ranges, the new set-point is found, and the procedure is successfully finished; (h) If however the properties of the output product are out allowed ranges, repeating the procedure from step b. according to one embodiment of the invention the calibration of the model comprises: (a) Taking the known model; (b) Substituting for the variables of the known model the latest set-point; (c) Predicting the values of the output properties; (d) Comparing the predicted output properties to the properties of the output product from the machine; (e) Updating the constants of the model to reduce the difference between predicted and measured properties to a negligible level.
According to another embodiment of the invention the calibration of the model comprises: (a) Taking the known model; (b) Providing to the machine an input set-point as calculated from the known model of the machine, for producing the goal product, and receiving an output product; (c) Substituting for the variables of the known model the latest set-point; (d) Predicting the values of the output properties; (e) Comparing the predicted output properties to the properties of the output product from the machine; (f) Updating the constants of the model to reduce the difference between predicted and measured properties to a negligible level.
According to one embodiment of the invention the optimization procedure comprises: (a) Taking the calibrated model; (b) Finding all set-points within the ranges of the possible machine set-points that, when substituted for the variables of the calibrated model, result in a product whose properties are predicted to be within allowed ranges for the properties of the output product; (c) From all the set-points found in step b, finding the optimal one, according to a defined set-point criteria.
Preferably, the optimal set-point criteria is selected from the following (a) Most robust set-point that will provide an output product whose variations with respect to errors in machine settings is minimal; (b) A set-point that is closest to the one used for updating the constants in step b of the main procedure; (c) A set-point whose values are closest to the center of the ranges of the possible machine set-points as defined in step a of the main procedure.
The invention further relates to a method for optimizing machine set-points in a group of machines of same type, which comprises: (a) Finding a new set-point for a first machine in the group, according to the main procedure; (b) Substituting for the variables of the known model the new set-point as found in step a, as the latest set-point for any other machine in the group.
The method of the invention can be used for an efficient tracking and optimizing of new set-points, to correct for changes in machine characteristics.
The method of the invention can be used for predicting a new set-point for correcting any change in the output properties of a product, wherein a latest set-point and one set of the previous product output properties obtained by operating the machine in said latest set-point, is used for obtaining a new set-point.
According to the invention the model can be of any type, including a physical model, a data based model, or a combination thereof.